Related papers: A Stratonovich-Skorohod integral formula for Volte…
Given a Gaussian process $X$, its canonical geometric rough path lift $\mathbf{X}$, and a solution $Y$ to the rough differential equation (RDE) $\mathrm{d}Y_{t} = V\left (Y_{t}\right ) \circ \mathrm{d} \mathbf{X}_t$, we present a…
In this paper we consider Skorohod and Stratonovich-type integrals in a general setting of Gaussian processes. We show that a conversion formula holds when the covariance functions of the Gaussian process are of finite $\rho$-variation for…
Given a continuous Gaussian process $x$ which gives rise to a $p$-geometric rough path for $p\in (2,3)$, and a general continuous process $y$ controlled by $x$, under proper conditions we establish the relationship between the Skorohod…
We derive explicit distance bounds for Stratonovich iterated integrals along two Gaussian processes (also known as signatures of Gaussian rough paths) based on the regularity assumption of their covariance functions. Similar estimates have…
Rough paths techniques give the ability to define solutions of stochastic differential equations driven by signals $X$ which are not semimartingales and whose $p$-variation is finite only for large values of $p$. In this context, rough…
We examine the relation between a stochastic version of the rough path integral with the symmetric-Stratonovich integral in the sense of regularization. Under mild regularity conditions in the sense of Malliavin calculus, we establish…
In this article, we derive a Stratonovich and Skorohod type change of variables formula for a multidimensional Gaussian process with low H\"older regularity (typically lower than 1/4). To this aim, we combine tools from rough paths theory…
We introduce a Skorokhod type integral and prove an Ito formula for a wide class of Gaussian processes which may exhibit stochastic discontinuities. Our Ito formula unifies and extends the classical one for general (i.e., possibly…
This paper develops an It\^o-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters \( H \in (\frac{1}{3}, \frac{1}{2}] \), using the Lyons' rough path framework. This approach is designed to fill…
We consider optimal approximation with respect to the mean square error of It\^o integrals and Skorohod integrals given an equidistant discretization of the Brownian motion. We obtain for suitable integrands optimal rates smaller than the…
We develop a general framework for pathwise stochastic integration that extends F\"ollmer's classical approach beyond gradient-type integrands and standard left-point Riemann sums and provides pathwise counterparts of It\^o, Stratonovich,…
Let the process Y(t) be a Skorohod integral process with respect to Brownian motion. We use a recent result by Tudor (2004), to prove that Y(t) can be represented as the limit of linear combinations of processes that are products of forward…
In this manuscript, we determine the optimal approximation rate for Skorohod integrals of sufficiently regular integrands. This generalizes the optimal approximation results for It\^o integrals. However, without adaptedness and the It\^o…
We derive a Gronwall type inequality for mild solutions of non-autonomous parabolic rough partial differential equations (RPDEs). This inequality together with an analysis of the Cameron-Martin space associated to the noise, allows us to…
We develop a Fourier approach to rough path integration, based on the series decomposition of continuous functions in terms of Schauder functions. Our approach is rather elementary, the main ingredient being a simple commutator estimate,…
This article gives an account on various aspects of stochastic calculus in the plane. Specifically, our aim is 3-fold: (i) Derive a pathwise change of variable formula for a path indexed by a square, satisfying some H\"older regularity…
We develop a stochastic analysis for a Gaussian process $X$ with singular covariance by an intrinsic procedure focusing on several examples such as covariance measure structure processes, bifractional Brownian motion, processes with…
We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is…
In this paper, we study rough path properties of stochastic integrals of It\^{o}'s type and Stratonovich's type with respect to $G$-Brownian motion. The roughness of $G$-Brownian Motion is estimated and then the pathwise Norris lemma in…
For a Gaussian process $X$ and smooth function $f$, we consider a Stratonovich integral of $f(X)$, defined as the weak limit, if it exists, of a sequence of Riemann sums. We give covariance conditions on $X$ such that the sequence converges…